Ability to set the `Copilot-Integration-Id` header for github-copilot provider

[elgreco247]

What you'd like to see

If you use a Personal Access Token (PAT) as your GITHUB_TOKEN and then try to use a github-copilot model, you will get a Bad Request response with the following error message:
Personal Access Tokens are not supported for this endpoint

This does not happen when the header Copilot-Integration-Id is set to the value copilot-developer-cli.

It would be nice if one could set the value of this header in the provider_opts object for github-copilot.

Why you'd like to see it

So that I can use my PAT when working with github-copilot models.

Workarounds?

Use a local models gateway.

[dgageot]

@elgreco247 could you give a try to #2475?

[elgreco247]

It worked when explicitly setting the copilot-integration-id value to copilot-developer-cli in the agent YAML file (the default value vscode-chat didn't work for me).

When switching copilot models in an interactive session, you still get the 400 responses; maybe this wouldn't be the case if it was possible to define the default value of copilot-integration-id with an environment variable or via user config?